Why does an invalid file successfully pass validation (C#)?

Good day to all! I ran into a problem that I can't properly connect the validation of the xml file via the xsd schema. The problem is that I have successfully validated a file that does not match the schema. I hope that knowledgeable people will be able to tell me where I made a mistake.

Scheme:

<?xml version="1.0" encoding="utf-8" ?>
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema">
  <xs:element name="books">
    <xs:complexType>
      <xs:sequence>
        <xs:element name="book">
          <xs:complexType>
            <xs:sequence>

              <xs:element name="name">
                <xs:simpleType>
                  <xs:restriction base="xs:string">
                    <xs:minLength value="1" />
                  </xs:restriction>
                </xs:simpleType>
              </xs:element>

              <xs:element name="author">
                <xs:simpleType>
                  <xs:restriction base="xs:string">
                    <xs:minLength value="1" />
                  </xs:restriction>
                </xs:simpleType>
              </xs:element>

              <xs:element name="price" type="xs:positiveInteger" />

              <xs:element name="id" type="xs:int" />
            </xs:sequence>
          </xs:complexType>
        </xs:element>        
      </xs:sequence>
    </xs:complexType>
    <xs:unique name='unique_field_id'>
      <xs:selector xpath='xs:book' />
      <xs:field xpath='id' />
    </xs:unique>
  </xs:element>
</xs:schema>

XML file that passes validation successfully:

<?xml version="1.0" encoding="utf-8"?>
<books xmlns="localhost" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="/XML/ BooksListSchema.xsd">
  <book xmlns="">
    <name></name>
    <author>Author 3</author>
    <price>3200</price>
    <id>1003</id>
  </book>
  <book xmlns="">
    <name>Book 4</name>
    <author>Author 4</author>
    <price>-3000</price>
    <id>547</id>
  </book>
  <book xmlns="">
    <name>Book 1</name>
    <author>Athour 11</author>
    <price>1111</price>
    <id>547</id>
  </book>
</books>

The code that checks the file for validity:

private void ValidaionFile (HttpPostedFileBase fileData) {
            string SchemaPath = Server.MapPath("~/XML/BooksListSchema.xsd");

            var xDoc = new XmlDocument();
            xDoc.Load(fileData.InputStream);

            xDoc.Schemas.Add("", SchemaPath);
            xDoc.Validate(ValidationEventHandler);
        }

        private static void ValidationEventHandler(object sender, ValidationEventArgs e) {
            XmlSeverityType type = XmlSeverityType.Warning;
            if (Enum.TryParse<XmlSeverityType>("Error", out type)) {
                if (type == XmlSeverityType.Error) throw new Exception(e.Message);
            }
        }